Circular Motion And Harmonic Motion

Front 1

angular velocity ω

Back 1

angle swept out / time
rad/s

Front 2

linear velocity, v

Back 2

rω
radius X angular velocity

Front 3

centripetal force

Back 3

the force acting towards the centre, that keeps an object moving in a circle
F = mrω^2 = mv^2/ r
mass, radius, angular velocity, linear velocity

Front 4

centripetal acceleration

Back 4

the acceleration acting towards the centre of a body moving in a circle

a= rω^2

Front 5

derivation of Keppler's Law T^2 ∝R^3

Back 5

v= d/t
v= 2πR/T........4π^2R^2/T^2 = v^2 (equation 1)
GMm/R^2 = mv^2/R (rearrange)
v^2 = GM/R (equation 2)
4π^2R^3/T^2 = GM/R.... T^2= 4π^2R^3/GM
T^2 ∝ R^3

Front 6

derivation of v = rω

Back 6

linear velocity = d/t
1 rev, vel = 2πR/T
v= RX 2π/T (where ω = 2π/T for 1 rev)
v=rω

Front 7

Hookes Law

Back 7

the restoring force is proportional to the extension of the spring (provided the elastic limit is not exceeded)
F is proportional to S
F = -KS

Front 8

a body is said to be moving with simple harmonic motion if...

Back 8

a) its acceleration is directly proportional to its distance from a fixed point on its path

b) its acceleration is always directed towards that point

Front 9

equation for simple harmonic motion

Back 9

- ω^2S

Front 10

to show that any object that obeys hooke's law will execute SHM

Back 10

F = -KS a= - ω^2S
ma= -KS
a= -K/M XS -K/M = ω^2
a = - ω^2S

Front 11

what is the period and amplitude of a pendulum

Back 11

Period, T = 2π√l/g
amplitude= maximum displacement